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\newtheorem{case}[theorem]{Case}
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\begin{document}
La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 5x-2\right\vert ,$ $g(x)=2x^{2}-3x$ es\medskip\newline\qquad a)
$\left\vert 10x^{3}-15x-2\right\vert $\qquad\qquad\qquad b) $\left\vert
5x^{3}-15x-2\right\vert \medskip$\newline\qquad c) $\left\vert 10x^{3}%
-10x-2\right\vert $\qquad\qquad\qquad d) $\left\vert 10x^{3}-15x-10\right\vert
$

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 3x-1\right\vert ,$ $g(x)=\sqrt{x^{2}-2}$ es\medskip\newline\qquad
a) $\left\vert \sqrt{9x^{2}-18}-1\right\vert $\qquad\qquad\qquad b)
$\left\vert \sqrt{9x^{2}-10}-1\right\vert \medskip$\newline\qquad c)
$\left\vert \sqrt{9x^{2}-18}-9\right\vert $\qquad\qquad\qquad d) $\left\vert
\sqrt{9x^{2}-18}-3\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert \dfrac{2x}{x-1}-1\right\vert ,$ $g(x)=$ $\sqrt{x^{3}-x^{2}+2}%
$es\medskip\newline\qquad a) $\left\vert \dfrac{\sqrt{4x^{3}-4x^{2}+8}}%
{\sqrt{x^{3}-x^{2}+2}-1}-1\right\vert $\qquad\qquad\qquad b) $\left\vert
\dfrac{\sqrt{2x^{3}-2x^{2}+4}}{\sqrt{x^{3}-x^{2}+2}-1}-1\right\vert \medskip
$\newline\qquad c) $\left\vert \dfrac{\sqrt{4x^{3}-4x^{2}-8}}{\sqrt
{x^{3}-x^{2}+2}-1}-1\right\vert $\qquad\qquad\qquad d) $\left\vert
\dfrac{\sqrt{4x^{3}-4x^{2}-8}}{\sqrt{x^{3}-x^{2}-2}-1}-1\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert \dfrac{5x}{x-2}-3\right\vert ,$ $g(x)=$ $\sqrt{x^{3}-x^{2}}%
$es\medskip\newline\qquad a) $\left\vert \dfrac{\sqrt{25x^{2}(x-1)}}%
{\sqrt{x^{2}\left(  x-1\right)  }-2}-3\right\vert $\qquad\qquad\qquad b)
$\left\vert \dfrac{\sqrt{5x^{2}(x-1)}}{\sqrt{x^{3}-x^{2}}-2}-3\right\vert
\medskip$\newline\qquad c) $\left\vert \dfrac{\sqrt{25x^{2}(x+1)}}{\sqrt
{x^{3}-x^{2}}-2}-3\right\vert $\qquad\qquad\qquad d) $\left\vert \dfrac
{\sqrt{25x^{2}(x-1)}}{\sqrt{x^{3}+x^{2}}-2}-3\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 2x-2\right\vert ,$ $g(x)=\sqrt{x^{2}-2}$ es\medskip\newline\qquad
a) $2\left\vert \sqrt{x^{2}-2}-1\right\vert $\qquad\qquad\qquad b)
$2\left\vert \sqrt{x^{2}-2}-2\right\vert \medskip$\newline\qquad c)
$2\left\vert \sqrt{x^{2}-1}-2\right\vert $\qquad\qquad\qquad d) $\left\vert
\sqrt{4x^{2}-4}-2\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert x-1\right\vert ,$ $g(x)=\sqrt{x^{2}-4}$ es \newline\qquad a)
$2\left\vert \sqrt{x^{2}-4}-1\right\vert \qquad$b) $2\left\vert \sqrt{x^{2}%
-1}+1\right\vert $\newline\qquad c) $2\left\vert \sqrt{x^{2}-3}\right\vert
$\qquad\qquad d) $\left\vert \sqrt{4x^{2}-4}-1\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 2x-4\right\vert ,$ $g(x)=\sqrt{3-x^{2}}$ es \newline\qquad a)
$2\left\vert \sqrt{3-x^{2}}-2\right\vert $\qquad b) $\left\vert \sqrt
{6-2x^{2}}-4\right\vert $\newline\qquad c) $2\left\vert \sqrt{3-x^{2}%
}-4\right\vert $\qquad d) $2\left\vert \sqrt{6-2x^{2}}-2\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 3x-3\right\vert ,$ $g(x)=\sqrt{x^{2}+1}$ es \newline\qquad a)
$3\left\vert \sqrt{x^{2}+1}-1\right\vert $\qquad b) $\left\vert \sqrt
{3x^{2}+3}-3\right\vert $\newline\qquad c) $3\left\vert \sqrt{3x^{2}%
+3}-1\right\vert $\qquad d) $3\left\vert \sqrt{x^{2}+1}-3\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 4x-32\right\vert ,$ $g(x)=\sqrt{x^{2}-3}$ es \newline\qquad a)
$4\left\vert \sqrt{x^{2}-3}-8\right\vert $\qquad b) $\left\vert \sqrt
{4x^{2}-12}-32\right\vert $\newline\qquad c) $\left\vert \sqrt{4x^{2}%
-12}-48\right\vert $\qquad d) $2\left\vert \sqrt{x^{2}-3}-8\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 5x-25\right\vert ,$ $g(x)=\sqrt{5-x^{2}}$ es \newline\qquad a)
$5\left\vert \sqrt{5-x^{2}}-5\right\vert $\qquad b) $\left\vert \sqrt
{25-x^{2}}-25\right\vert $\newline\qquad c) $\left\vert 5\sqrt{5-x^{2}%
}-5\right\vert $\qquad d) $5\left\vert \sqrt{5-x^{2}}-25\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 6x-36\right\vert ,$ $g(x)=\sqrt{3-x^{2}}$ es \newline\qquad a)
$6\left\vert \sqrt{3-x^{2}}-6\right\vert $\qquad$\ $b) $\left\vert
6\sqrt{3-x^{2}}-36\right\vert $\newline\qquad c) $6\left\vert \sqrt{3-x^{2}%
}-36\right\vert $\qquad d) $\left\vert \sqrt{18-6x^{2}}-36\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 21x-7\right\vert ,$ $g(x)=\sqrt{x^{5}-7}$ es \newline\qquad a)
$7\left\vert 3\sqrt{x^{5}-7}-1\right\vert $\qquad b) $7\left\vert \sqrt
{3x^{5}-21}-1\right\vert $\newline\qquad c) $\left\vert \sqrt{21x^{2}%
-147}-7\right\vert $\qquad d) $\left\vert \sqrt{21x^{2}-147}-49\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 48x-40\right\vert ,$ $g(x)=\sqrt{9-x^{2}}$ es \newline\qquad a)
$8\left\vert 6\sqrt{9-x^{2}}-5\right\vert $\qquad b) $8\left\vert
\sqrt{54-6x^{2}}-5\right\vert $\newline\qquad c) $\left\vert \sqrt
{432-48x^{2}}-320\right\vert $\qquad d) $\left\vert \sqrt{432-48x^{2}%
}-40\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 90x-99\right\vert ,$ $g(x)=\sqrt{x^{2}-3}$ es \newline\qquad a)
$9\left\vert 10\sqrt{x^{2}-3}-11\right\vert \qquad$b) $9\left\vert
\sqrt{10x^{2}-30}-11\right\vert $\newline\qquad c) $9\left\vert \sqrt
{10x^{2}-30}-110\right\vert $\qquad d) $\left\vert \sqrt{90x^{2}%
-270}-99\right\vert $

La funci\'{o}n composici\'{o}n $\ f\circ g$ de las funciones $\ f(x)=$
$\left\vert 90x-100\right\vert ,$ $g(x)=\sqrt{8-x^{2}}$ es \newline\qquad a)
$10\left\vert 9\sqrt{8-x^{2}}-10\right\vert $\qquad b) $\left\vert
\sqrt{720-90x^{2}}-100\right\vert $\newline\qquad c) $10\left\vert
\sqrt{72-9x^{2}}-90\right\vert $\qquad d) $10\left\vert \sqrt{72-9x^{2}%
}-10\right\vert $


\end{document}